Question

size of a image of an object formed by a mirror having a focal length of 20 cm is observed to be reduce one third of its size .At what distance the object has ben placed from the mirror? what is the nature of the image and the mirror​

Answer 1

Answer:

f=+20 cm. v=-u/3. i/f=1/v+1/u. therefore, u= -40 cm.

Answer 2

Answer:

HII!

lets see the answer in cases!1

CASE 1:-  m=-1/3(in case of concave mirror)

f= -20 cm

m= -1/3 =-v/u

v=u/3

1/f= 1/v +1/u .

=> -1/20 = 3/u + 1/ u= 4/u

therefore.,, u = -80 cm.

CASE 2:-

M=+1/3 (IN CASE OF CONVEX MIRROR)

f=+20 cm.

m=+1/3 =-v/u

v=-u/3.

i/f=1/v+1/u.

=> 1/20= -3/4 + 1/4 =-2/4

therefore, u= -40 cm.

hope it helps!!

please mark as brainliest

thank you!!

OR....

As we know, m = - v/u = h₁/h₂

⇒ - v/u = 1/3 h₂/h₂

⇒ u = - 3v

Applying mirror formula,

1/v + 1/u = 1/f, we get

when f = + 20 cm

⇒ 1/v - 1/3v = 1/20

⇒ 3 - 1/3v = 1/20

⇒ 2/3v = 1/20

⇒ 3v = 2 × 20

⇒ v = 2 × 30/3

⇒ v = 40/3 .. (i)

u = - 3v

By putting v value, we get

⇒ u = - 3 × 40/3

⇒ u = - 40 cm.

Object Distance = - 40 cm

If we take f = - 20 cm, value of u will be + 40 cm which is not possible.

m = - v/v

⇒ m = - 40/3/- 40

⇒ m = + 1/3

⇒ m = 0.33 cm

This implies that the nature of the image is erect and diminished.

Nature of Image = Convex Mirror.